Strong-weak Stackelberg Problems in Finite Dimensional Spaces

We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present some approximation results when the parameter ǫ goes to zero. Finally, as an example, we consider an optimization problem associated to a best bound given in [2] for a system of nondifferentiable convex inequalities.

On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes

Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.

Medical students' personal experience of high-stakes failure:case studies using interpretative phenomenological analysis

Abstract (provisional): Background Failing a high-stakes assessment at medical school is a major event for those who go through the experience. Students who fail at medical school may be more likely to struggle in professional practice, therefore helping individuals overcome problems and respond appropriately is important. There is little understanding about what factors influence how individuals experience failure or make sense of the failing experience in remediation. The aim of this study was to investigate the complexity surrounding the failure experience from the student’s perspective using interpretative phenomenological analysis (IPA). Methods The accounts of 3 medical students who had failed final re-sit exams, were subjected to in-depth analysis using IPA methodology. IPA was used to analyse each transcript case-by-case allowing the researcher to make sense of the participant’s subjective world. The analysis process allowed the complexity surrounding the failure to be highlighted, alongside a narrative describing how students made sense of the experience. Results The circumstances surrounding students as they approached assessment and experienced failure at finals were a complex interaction between academic problems, personal problems (specifically finance and relationships), strained relationships with friends, family or faculty, and various mental health problems. Each student experienced multi-dimensional issues, each with their own individual combination of problems, but experienced remediation as a one-dimensional intervention with focus only on improving performance in written exams. What these students needed to be included was help with clinical skills, plus social and emotional support. Fear of termination of the their course was a barrier to open communication with staff. Conclusions These students’ experience of failure was complex. The experience of remediation is influenced by the way in which students make sense of failing. Generic remediation programmes may fail to meet the needs of students for whom personal, social and mental health issues are a part of the picture.

Spatiotemporal optical bullets in two-dimensional fiber arrays and their stability

Long-lived light bullets fully localized in both space and time can be generated in novel photonic media such as multicore optical fiber or waveguide arrays. In this paper we present detailed theoretical analysis on the existence and stability of the discrete-continuous light bullets using a very generic model that occurs in a number of applications.

Integrated Dimensional Variation Management in the Digital Factory

This paper describes how dimensional variation management could be integrated throughout design, manufacture and verification, to improve quality while reducing cycle times and manufacturing cost in the Digital Factory environment. Initially variation analysis is used to optimize tolerances during product and tooling design and also results in the creation of a simplified representation of product key characteristics. This simplified representation can then be used to carry out measurability analysis and process simulation. The link established between the variation analysis model and measurement processes can subsequently be used throughout the production process to automatically update the variation analysis model in real time with measurement data. This ‘live’ simulation of variation during manufacture will allow early detection of quality issues and facilitate autonomous measurement assisted processes such as predictive shimming. A study is described showing how these principles can be demonstrated using commercially available software combined with a number of prototype applications operating as discrete modules. The commercially available modules include Catia/Delmia for product and process design, 3DCS for variation analysis and Spatial Analyzer for measurement simulation. Prototype modules are used to carry out measurability analysis and instrument selection. Realizing the full potential of Metrology in the Digital Factory will require that these modules are integrated and software architecture to facilitate this is described. Crucially this integration must facilitate the use of realtime metrology data describing the emerging assembly to update the digital model.

The Legendre Formula in Clifford Analysis

2000 Mathematics Subject Classification: 30A05, 33E05, 30G30, 30G35, 33E20.

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.

Universal profile of the vortex condensate in two-dimensional turbulence

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate—a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.

Learning user and product distributed representations using a sequence model for sentiment analysis

In product reviews, it is observed that the distribution of polarity ratings over reviews written by different users or evaluated based on different products are often skewed in the real world. As such, incorporating user and product information would be helpful for the task of sentiment classification of reviews. However, existing approaches ignored the temporal nature of reviews posted by the same user or evaluated on the same product. We argue that the temporal relations of reviews might be potentially useful for learning user and product embedding and thus propose employing a sequence model to embed these temporal relations into user and product representations so as to improve the performance of document-level sentiment analysis. Specifically, we first learn a distributed representation of each review by a one-dimensional convolutional neural network. Then, taking these representations as pretrained vectors, we use a recurrent neural network with gated recurrent units to learn distributed representations of users and products. Finally, we feed the user, product and review representations into a machine learning classifier for sentiment classification. Our approach has been evaluated on three large-scale review datasets from the IMDB and Yelp. Experimental results show that: (1) sequence modeling for the purposes of distributed user and product representation learning can improve the performance of document-level sentiment classification; (2) the proposed approach achieves state-of-The-Art results on these benchmark datasets.

Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

Next generation high density three-dimensional magnetic recording systems

This work is the first work using patterned soft underlayers in multilevel three-dimensional vertical magnetic data storage systems. The motivation stems from an exponentially growing information stockpile, and a corresponding need for more efficient storage devices with higher density. The world information stockpile currently exceeds 150EB (ExaByte=1x1018Bytes); most of which is in analog form. Among the storage technologies (semiconductor, optical and magnetic), magnetic hard disk drives are posed to occupy a big role in personal, network as well as corporate storage. However; this mode suffers from a limit known as the Superparamagnetic limit; which limits achievable areal density due to fundamental quantum mechanical stability requirements. There are many viable techniques considered to defer superparamagnetism into the 100's of Gbit/in2 such as: patterned media, Heat-Assisted Magnetic Recording (HAMR), Self Organized Magnetic Arrays (SOMA), antiferromagnetically coupled structures (AFC), and perpendicular magnetic recording. Nonetheless, these techniques utilize a single magnetic layer; and can thusly be viewed as two-dimensional in nature. In this work a novel three-dimensional vertical magnetic recording approach is proposed. This approach utilizes the entire thickness of a magnetic multilayer structure to store information; with potential areal density well into the Tbit/in2 regime. ^ There are several possible implementations for 3D magnetic recording; each presenting its own set of requirements, merits and challenges. The issues and considerations pertaining to the development of such systems will be examined, and analyzed using empirical and numerical analysis techniques. Two novel key approaches are proposed and developed: (1) Patterned soft underlayer (SUL) which allows for enhanced recording of thicker media, (2) A combinatorial approach for 3D media development that facilitates concurrent investigation of various film parameters on a predefined performance metric. A case study is presented using combinatorial overcoats of Tantalum and Zirconium Oxides for corrosion protection in magnetic media. ^ Feasibility of 3D recording is demonstrated, and an emphasis on 3D media development is emphasized as a key prerequisite. Patterned SUL shows significant enhancement over conventional "un-patterned" SUL, and shows that geometry can be used as a design tool to achieve favorable field distribution where magnetic storage and magnetic phenomena are involved. ^

Comparative study of dissolved organic matter from groundwater and surface water in the Florida coastal Everglades using multi-dimensional spectrofluorometry combined with multivariate statistics

Dissolved organic matter (DOM) in groundwater and surface water samples from the Florida coastal Everglades were studied using excitation–emission matrix fluorescence modeled through parallel factor analysis (EEM-PARAFAC). DOM in both surface and groundwater from the eastern Everglades S332 basin reflected a terrestrial-derived fingerprint through dominantly higher abundances of humic-like PARAFAC components. In contrast, surface water DOM from northeastern Florida Bay featured a microbial-derived DOM signature based on the higher abundance of microbial humic-like and protein-like components consistent with its marine source. Surprisingly, groundwater DOM from northeastern Florida Bay reflected a terrestrial-derived source except for samples from central Florida Bay well, which mirrored a combination of terrestrial and marine end-member origin. Furthermore, surface water and groundwater displayed effects of different degradation pathways such as photodegradation and biodegradation as exemplified by two PARAFAC components seemingly indicative of such degradation processes. Finally, Principal Component Analysis of the EEM-PARAFAC data was able to distinguish and classify most of the samples according to DOM origins and degradation processes experienced, except for a small overlap of S332 surface water and groundwater, implying rather active surface-to-ground water interaction in some sites particularly during the rainy season. This study highlights that EEM-PARAFAC could be used successfully to trace and differentiate DOM from diverse sources across both horizontal and vertical flow profiles, and as such could be a convenient and useful tool for the better understanding of hydrological interactions and carbon biogeochemical cycling.

Optimization of three-dimensional branching networks of microchannels for thermal management of microelectronics

The aim of this work is to present a methodology to develop cost-effective thermal management solutions for microelectronic devices, capable of removing maximum amount of heat and delivering maximally uniform temperature distributions. The topological and geometrical characteristics of multiple-story three-dimensional branching networks of microchannels were developed using multi-objective optimization. A conjugate heat transfer analysis software package and an automatic 3D microchannel network generator were developed and coupled with a modified version of a particle-swarm optimization algorithm with a goal of creating a design tool for 3D networks of optimized coolant flow passages. Numerical algorithms in the conjugate heat transfer solution package include a quasi-ID thermo-fluid solver and a steady heat diffusion solver, which were validated against results from high-fidelity Navier-Stokes equations solver and analytical solutions for basic fluid dynamics test cases. Pareto-optimal solutions demonstrate that thermal loads of up to 500 W/cm2 can be managed with 3D microchannel networks, with pumping power requirements up to 50% lower with respect to currently used high-performance cooling technologies.

Advanced thermal analysis of microelectronics using spreading resistance models

Thermal analysis of electronic devices is one of the most important steps for designing of modern devices. Precise thermal analysis is essential for designing an effective thermal management system of modern electronic devices such as batteries, LEDs, microelectronics, ICs, circuit boards, semiconductors and heat spreaders. For having a precise thermal analysis, the temperature profile and thermal spreading resistance of the device should be calculated by considering the geometry, property and boundary conditions. Thermal spreading resistance occurs when heat enters through a portion of a surface and flows by conduction. It is the primary source of thermal resistance when heat flows from a tiny heat source to a thin and wide heat spreader. In this thesis, analytical models for modeling the temperature behavior and thermal resistance in some common geometries of microelectronic devices such as heat channels and heat tubes are investigated. Different boundary conditions for the system are considered. Along the source plane, a combination of discretely specified heat flux, specified temperatures and adiabatic condition are studied. Along the walls of the system, adiabatic or convective cooling boundary conditions are assumed. Along the sink plane, convective cooling with constant or variable heat transfer coefficient are considered. Also, the effect of orthotropic properties is discussed. This thesis contains nine chapters. Chapter one is the introduction and shows the concepts of thermal spreading resistance besides the originality and importance of the work. Chapter two reviews the literatures on the thermal spreading resistance in the past fifty years with a focus on the recent advances. In chapters three and four, thermal resistance of a twodimensional flux channel with non-uniform convection coefficient in the heat sink plane is studied. The non-uniform convection is modeled by using two functions than can simulate a wide variety of different heat sink configurations. In chapter five, a non-symmetrical flux channel with different heat transfer coefficient along the right and left edges and sink plane is analytically modeled. Due to the edge cooling and non-symmetry, the eigenvalues of the system are defined using the heat transfer coefficient on both edges and for satisfying the orthogonality condition, a normalized function is calculated. In chapter six, thermal behavior of two-dimensional rectangular flux channel with arbitrary boundary conditions on the source plane is presented. The boundary condition along the source plane can be a combination of the first kind boundary condition (Dirichlet or prescribed temperature) and the second kind boundary condition (Neumann or prescribed heat flux). The proposed solution can be used for modeling the flux channels with numerous different source plane boundary conditions without any limitations in the number and position of heat sources. In chapter seven, temperature profile of a circular flux tube with discretely specified boundary conditions along the source plane is presented. Also, the effect of orthotropic properties are discussed. In chapter 8, a three-dimensional rectangular flux channel with a non-uniform heat convection along the heat sink plane is analytically modeled. In chapter nine, a summary of the achievements is presented and some systems are proposed for the future studies. It is worth mentioning that all the models and case studies in the thesis are compared with the Finite Element Method (FEM).

Three-dimensional tomographic reconstruction of an exceptionally well preserved ichnological assemblage from the Stainmore Foundation, Carboniferous, UK

This Ph.D. thesis addresses current issues with ichnotaxonomic practice, and characterizes an exceptionally well preserved ichnological assemblage from the Carboniferous Stainmore Formation, Northumberland, United Kingdom. Samples were collected from closely localized float representative of various units throughout the succession, which was deposited in a storm-dominated marine shoreface. Three dominant ichnotaxa were selected for three-dimensional morphological analysis due to their complicated morphology and/or unclear taxonomic status: 1) Dactyloidites jordii isp. nov.; 2) Beaconites capronus, and; 3) Neoeione moniliformis comb. nov. Using serial grinding and photography, these ichnotaxa were ground and modelled in true colour. High-resolution models of three taxa produced in this study are the basis of the first complete three-dimensional consideration of the traces, and forms the basis for refined palaeobiological and ethological analysis of these taxa. Dactyloidites jordii isp. nov. is a stellate to palmate burrow composed of numerous long, narrow rays that exhibit three orders of branching arranged into tiered galleries radiating from a central shaft. It is considered to be the feeding structure produced by a vermiform organism. Beaconites capronus is a winding trace with distinctly chevron-shaped, meniscate backfill demonstrated herein to backfill the vertical shafts associated with its burrows in a comparable fashion to the horizontal portion of the burrow. This lack of a surface connection would result in the trace making organism being exposed to low-oxygen porewater. Coping with this porewater dysoxia could be approached by burrowing organisms in a number of ways: 1) revisiting the sediment-water interface; 2) creating periodic shafts; or 3) employing anaerobic metabolism. Neoeione moniliformis was originally introduced as Eione moniliformis, however, the genus Eione Tate, 1859 is a junior homonym of Eione Rafinesque, 1814. This led to the transfer of Eione moniliformis to Parataenidium. Through careful examination and three-dimensional characterization of topotypes, the transfer to Parataenidium moniliformis is demonstrated herein to be problematic, as Parataenidium refers to primarily horizontal burrows with two distinct layers and Eione moniliformis is composed of one distinct level. As such, the new ichnogenus Neoeione is created to accommodate Neoeione moniliformis.